芯径渐缩光纤对孤子传输的影响

EFFECT ON SOLITON PROPAGATION IN CORE RADIUM DECREASING FIBER

通过芯径渐缩、指数型连续渐缩或阶梯型离散渐缩的方法，可获得色散随距离下降的光纤，能补偿光纤损耗对孤子传输的影响。但芯径的连续变化，将导致模耦合。分析发现，在连续渐缩光纤中，即使Ｖ＜２．４０４８始终满足，仍可存在两种模式：其一是Ｚ→∞的稳态模，另一为兼有导模和辐射模部分性质的一种特殊模式，称为“过渡模”，该模式的模式场是一系列ＬＰ０ｍ′的模式场的迭加，它包括导模ＬＰ０１′的模式场和辐射模ＬＰ０ｍ′（ｍ≥２）的模式场，随着ｒ→∞不是迅速衰减而是振荡着缓慢衰减。它具有与激励模相同的传输常数，但幅度却以芯径渐缩的速率衰减。尽管指数型渐缩光纤可增加孤子的传输距离，但“过渡模”的影响始终存在，而离散型光纤不存在“过渡模”。为了估计稳态模的基态孤子在芯径渐缩光纤中的传输长度，可利用该模的本地功率与阈值功率之比来计算，称该比值为“裕度”。如果在进入渐缩光纤之前，基态孤子已经处于阈值临界状态，则在渐缩光纤中稳态模孤子的裕度恰好等于孤子阶数参量Ｎ２的变化比。本文给出了在高斯近似下的过渡模和稳态模的功率计算公式。

Fiber which dispersion decreases with distance in exponential power can overcome the effect induced by loss on soliton propagation. We can obtain this character by using core radium decreasing fiber, exponentially continual decreasing or discrete decreasing (ladder fiber ).Continual variation of radium will produce modes coupling. After analyses, in the continual core radium decreasing fiber, even if v<2.4048, there will still be two modes. One is stable mode when z→∞ , the other is a special mode with both characters of transmission mode and of radiation mode which we called it transition mode. It has the same transmission constant as the exciting mode, but its amplitude reduces at the decreasing ratio of core radium. The effect of transition mode always exists in the exponential decreasing fiber,in spite that it can efficiently increase the distance of soliton propagation. There is no transition mode in the ladder fiber, but each section of this fiber will be shorter. In order to evaluate the transmission distance of the stable mode ground state soliton, we calculate it with the ratio of local power and threshold power, and call it threshold degree. If the ground state soliton has the power of threshold before entering the core radium decreasing fiber, the threshold degree of stable soliton is equal to the ratio of the order parameter of soliton N 2. Difference of the threshold degree between ladder fiber and exponential fiber is so little that there is almost no distinctness between them. The formula and curves of the threshold degree are given at the end of this article, which mean the preceeding transmission distance in fibers.